I assume you mean for the fluid to also be irrotational, and for u to be the fluid potential. Is that right? Then you should have [itex]\vec V = \nabla u[/itex], although from the next two lines it seems like you know this, and the above was a typo.

Technically the curl can only be taken of a vector field, and it is another vector field, and this operation is only defined in 3D. You can use the curl in 2D if you think of your 2D space as a plane in a larger 3D space. Then the curl of any vector field in the plane is perpendicular to the plane (ie, something times [itex]\hat k[/itex]), and so may be treated as a scalar (this happens with the vorticity [itex]\vec \omega[/itex]). Conversely, if you have a vector field that is everywhere normal to the plane, it may be treated as a scalar, and its curl is a vector field in the plane. This latter case is what happens with the stream function. Also, I think you want to set the velocity, not the potential, equal to the curl of the stream function.